Disruption of Thermally-Stable Nanoscale Grain Structures by
Strain Localization
Amirhossein Khalajhedayati a, Timothy J. Rupert a,b,*
a
Department of Chemical Engineering and Materials Science, University of California, Irvine,
CA 92697, USA
b
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA
92697, USA
*
Email Address: [email protected] (T.J. Rupert).
Nanocrystalline metals with average grain sizes of only a few nanometers have recently been
observed to fail through the formation of shear bands. Here, we investigate this phenomenon in
nanocrystalline Ni which has had its grain structure stabilized by doping with W, with a specific
focus on understanding how strain localization drives evolution of the nanoscale grain structure.
Shear banding was initiated with both microcompression and nanoindentation experiments,
followed by site-specific transmission electron microscopy to characterize the microstructure.
Grain growth and texture formation were observed inside the shear bands, which had a wide
variety of thicknesses. These evolved regions have well-defined edges, which rules out local
temperature rise as a possible formation mechanism. No structural evolution was found in areas
away from the shear bands, even in locations where significant plastic deformation had occurred,
showing that plastic strain alone is not enough to cause evolution.
Rather, intense strain
localization is needed to induce mechanically-driven grain growth in a thermally-stable
nanocrystalline alloy.
1
In recent years, studies have shown that plastic deformation is very different in
nanocrystalline metals when compared to traditional microcrystalline materials1. In conventional
metallurgical theory, grain boundaries are seen as obstacles to intergranular dislocation motion.
However, recent studies have shown that the grain refinement to nanometer scale shifts the
sources of plastic deformation from inside the crystals to the interfacial regions themselves2,3.
Dislocations created and subsequently absorbed at grain boundaries become the main source of
plastic deformation in nanocrystalline metals with average grain sizes (d) between 100 nm and
10 nm. Further refinement of the grains below 10 nm confines plasticity almost entirely to the
grain boundaries, with grain boundary migration and grain rotation/sliding as the major events
that contribute to plastic deformation4.
As a result of these novel deformation mechanisms, Schuh and Lund5 suggested that
nanocrystalline systems with d < 10 nm should have mechanical properties which resemble
those of metallic glasses.
This concept was first supported by the observation that
nanocrystalline metals exhibit a tension-compression asymmetry of their strength and shear
transformation zones operate inside of grain boundary regions during plasticity6.
Recent
molecular dynamics (MD) simulations7 have uncovered a universal relation between strength
and modulus in nanocrystalline alloys that resembles prior observations of metallic glasses8.
Another connection between the mechanical behavior of metallic glasses and nanocrystalline
metals was found when Trelewicz and Schuh9 explored the plasticity of nanocrystalline Ni-W
using nanoindentation and found shear steps in the pileup surrounding the indents for average
grain sizes of 6 nm and 3 nm, with more significant steps observed in the finer grained sample.
The shear offsets observed in this study were similar to observations from the metallic glass
literature, such as the shear banding found after nanoindentation of an Al-based metallic glass by
2
Jiang et al.10. In a more recent study of nanocrystalline Ni-W, Khalajhedayati and Rupert11
observed that shear banding is more prominent during uniaxial compression, which does not
impose the confining hydrostatic pressure found in nanoindentation. In this case, shear banding
was found in grain sizes as large as 15 nm, suggesting that catastrophic strain localization can be
a more common problem for nanocrystalline materials than previously thought and that this
phenomenon must be more thoroughly studied.
When shear banding is observed in metallic glasses, it is often accompanied by structural
evolution, most commonly in the form of crystallite formation12,13. However, the effect of shear
banding on the structure of nanocrystalline materials has not been explored thoroughly, with
experimental evidence especially scarce. Wei and coworkers did observe grain coarsening inside
of shear bands in ultra-fine grained (typically meaning 100 nm < d < 1000 nm) Fe with d of 110
nm 14, as well as ultra-fine grained W15 and Ta16. However, these materials have average grain
sizes that are larger than what would be considered nanocrystalline and were all body centered
cubic (BCC) metals, meaning a direct extrapolation to nanocrystalline face centered cubic (FCC)
metals such as Cu, Al, or Ni is not possible. Some insight has been provided by MD simulations,
but these studies have been limited to pure, single element metals. For example, Sansoz and
Dupant17 studied nanoindentation of nanocrystalline Al with d = 5 nm and d = 7 nm at absolute
zero temperature and reported grain growth due to grain rotation and grain boundary migration
inside of shear bands. More recently, Rupert18 observed the formation of shear bands during
simulated tensile testing of a nanocrystalline Ni with d = 3 and 6 nm using MD. These studies
show that the grain structure in pure nanocrystalline materials can be considered dynamic under
mechanical loading.
3
However, alloying with a second element is often required in practice, since pure
nanocrystalline metals can undergo thermally-driven grain growth even at room temperature in
some cases19. Chookajorn et al.20 showed that reducing grain boundary energy by doping these
interfaces can be a powerful design strategy for the creation of thermally-stable nanocrystalline
materials, demonstrating this concept by producing a W-20 at.% Ti alloy that retained a 20 nm
grain size even after being exposed to 1000 °C for one week. An exemplary material system that
uses this concept of grain boundary dopants to its advantage is nanocrystalline Ni-W. Detor and
Schuh21 created thermally-stable Ni-W alloys with grain sizes ranging from ~140 nm down to ~3
nm, tuned by controlling the W concentration, using electrodeposition. Recent studies have
shown that alloying can also change a nanocrystalline materials resistance to mechanicallydriven structural evolution. For example, extremely pure nanocrystalline Al was observed to
experience dramatic grain coarsening under uniaxial loading22, but the addition of small amounts
of O into such films stabilized the grain structure23. Similarly, Lohmiller et al.24 found that pure
Au is prone to stress-induced grain growth, while Au with Cu segregated to the grain boundaries
is not. From these studies, it is clear that doping can increase the stability of nanocrystalline
grain structures, at least to evolution caused by temperature or simple stress states. However, the
impact of the extreme deformation conditions which occur during shear banding has not been
explored. Specifically, it would be useful to understand if the extreme deformation that occurs
during shear banding can overcome the enhanced structural stability brought by alloying
additions and if teven heavily doped grain structures can evolve under mechanical loading.
In this study, we investigate the microstructure of nanocrystalline Ni-W with d = 5 nm
before and after catastrophic shear banding. Ni-W was chosen as a model system for this study
because, due to the subtle tendency for segregation of W to the grain boundaries (grain boundary
4
excesses of 4-8 at.% W over the grain interior composition), nanocrystalline coatings that are
resistant to thermal grain growth up to ~500 °C (i.e., ~45% of the melting temperature) can be
created25. This allows us to observe how severe strain localization occurs in an alloy system
which is typically stable. A combination of microcompression and nanoindentation were used to
induce shear banding, since these two techniques allow us to explore different stress states and
plastic strain distributions. During microcompression, nearly all plastic strain is limited to the
shear bands, while in nanoindentation there is a combination of shear banding and homogeneous
plasticity. We find that intense strain localization inside of shear bands can drive obvious
coarsening and texturing, while homogeneous plasticity (or low plastic strain) leaves the grain
structure unchanged. These results suggest that even thermally-stable nanocrystalline grain
structures can coarsen under mechanical loading, but extreme conditions are required.
Results
Microcompression of nanocrystalline Ni-W with d = 5 nm. Figure 1a shows a scanning
electron microscope (SEM) image of a micropillar of nanocrystalline Ni-W after
microcompression testing. The pillar experienced a large strain burst and failed catastrophically.
The micropillar has a number of major surface steps corresponding to primary shear bands (red
arrow), with a high density of thinner, secondary shear bands that crisscross each other also
observed (white arrow). Figure 1b shows the corresponding true stress-strain curve for this
pillar. Several strain bursts are observed in this curve, with two examples denoted by black
arrows. The pillar compresses elastically for the majority of this test, with deviations from this
behavior only coming in the form of strain bursts. Such a response is a sign that plasticity is
5
dominated by shear banding for this testing methodology, not homogeneous plastic deformation,
as a smooth microplastic region of the stress-strain curve would be found in that case.
Figure 2a presents a bright field TEM image of shear bands, one primary and one
secondary, inside of the micropillar. Shear bands with thicknesses from 10 to 270 nm were
observed, and most of the shear bands are in the lower end of this range. The thickest bands
corresponded to locations where large, primary shear bands were found on the surface, with an
example found in the center of Figure 2a and denoted by dashed white lines. A smaller,
secondary shear band is found in the lower right of the same figure outlined by solid white lines.
This figure also shows that grain growth is limited to the shear bands. Figure 2b shows a
magnified view of the microstructure inside of the major shear band, with the largest grains in
this region being ~17 nm in diameter. Figure 2c shows the cumulative distribution function of
grain size inside and outside the shear bands, as compared to the as-deposited microstructure.
The average grain size inside the shear bands has been increased by more than 50%, from 5 nm
to about 8 nm, and the distribution of grain sizes has widened. The grain size outside of the
shear bands, in the region which only experienced elastic deformation, has not changed and the
grain size distribution follows the same pattern as the initial microstructure. An example of the
network of shear bands found inside the sample is shown in Figure 2d. Part of a primary shear
band can be seen in the top left of the image, with many secondary shear bands coming out in
directions downward and to the right. The crisscross pattern seen on the surface of the pillar in
the regions with a high density of secondary shear bands has a similar appearance. All shear
bands observed in microcompression samples appeared as long, straight lines. To the best of our
knowledge, this is the first time that the microstructure inside of a shear band has been observed
experimentally in a nanocrystalline FCC metal.
6
Figure 3a presents a selected area electron diffraction pattern taken from one of the major
shear bands. The segmented ring pattern is indicative of a textured microstructure and the
specific pattern observed here is a pure shear texture often observed in FCC metals, consisting of
{100} <011>, {111} <112>, and {111} <110> components26. Similar patterns and textures
were found along the entire length of the shear band, confirming that this observation was a
general one. A dark field image, taken by putting the smallest objective aperture on one of the
segmented rings, is shown in Figure 3b.
Grains that are oriented in the same diffraction
condition are visible as bright spots in this image, with the high density of bright regions inside
the shear band indicating the existence of a preferred orientation. Outside the shear band, the
distribution of dark and bright spots is random since there is no texture. Figure 3c shows a
higher magnification dark field TEM image of the microstructure inside the same shear band,
where a cluster of grains with the same orientation can be seen.
Nanoindentation of nanocrystalline Ni-W with d = 5 nm. Nanoindentation imposes a strong
strain gradient and a complex stress field under the indenter tip27.
Figure 4a shows a
nanoindentation made with a cube corner tip. The tip geometry literally resembles the corner of
a cube and has a very sharp end, therefore it confines the plasticity to a small volume of material
under the tip and often induces pile-up formation around the indents. The large shear steps that
are observed in the pile-up surrounding the nanoindentation site in this figure indicate that
inhomogeneous plasticity and flow localization occurred28. Figure 4b shows the corresponding
load-displacement curve from this nanoindentation experiment. The nanoindenter is inherently
force-controlled, so any shear banding events appear as a burst in displacement11. Two such
displacement bursts are magnified in Figure 4b, each with a magnitude of ~10-15 nm.
7
An indentation study by Wright et al. on Zr based metallic glass showed that flow
serration during loading is due to formation of shear bands under the indenter tip29. Although
these serrations clearly exist in our experiment, careful examination shows that the loading curve
is mostly smooth and only a few displacement bursts are observed. Another way to visualize the
number of the shear band events is to plot the instantaneous strain rate versus indentation depth,
as shown in Figure 4c. Since the indentation test was supposed to be at a constant strain rate
under perfect conditions (i.e., without any displacement bursts), the strain rate data should follow
a straight line. However, the displacement bursts that occur in this experiment lead to local
peaks in the instantaneous strain rate. The peaks that are pointed out here correspond to the same
displacement bursts that were highlighted in the load-displacement curve, and less than 10 of
these peaks were observed. The deformation is a combination of homogenous plasticity (smooth
load-displacement curve) and strain localization (displacement bursts).
Schuh and Nieh30
observed similar combinations of deformation modes in Pd- and Zr-based metallic glasses.
Figure 5a shows cross-sectional TEM images of the nanoindentation observed in the
previous figure. The area under the indenter tip denoted by a dashed box is magnified in Figure
5b. The shear bands have a curved shape and extend deep under the indenter tip, in contrast to
the straight shear bands found after microcompression. Measurement of the shear bands after
indentation showed that the thickness varies from 8 nm to 32 nm. The area denoted with a solid
white box is magnified in Figure 5c. Grain growth was observed in all the shear bands but, due
to limited thickness of the shear bands in nanoindentation, selected area diffraction patterns
could not give conclusive results about the texture. Figure 5c shows the shear bands that extend
to the pile-up surrounding the indentation site. These bands terminate at the surface and result in
slip steps there, as previously shown from a different perspective in Figure 4a. Figure 6a shows
8
an example of the complex, entangled pattern of curved shear bands formed under the indent.
Figure 6b presents the cumulative distribution function of grain size for the sample which was
indented. The grain size distribution outside of the shear bands remained the same as the asdeposited specimen. However, the grain size inside the shear bands is much larger, with d
increasing from 5 nm to 8 nm and a distribution which ranged from 3-17 nm.
Discussion
The experiments described above show that nanocrystalline alloys with extremely fine
grain sizes can experience strain localization in the form of shear banding, mimicking prior
observations in metallic glasses. This similarity can be understood by recognizing the features
these materials have in common. Both metallic glasses and nanocrystalline metals are extremely
strong, which has been shown to be important for strain localization3,31. If the ratio of strain
hardening rate to the applied stress drops below a critical value, a material can be prone to flow
localization32. In both nanocrystalline metals and metallic glasses, the applied stresses are
extremely high and strain hardening is almost nonexistent, satisfying these conditions.
In
addition, both classes of materials are unable to store large numbers of dislocations and achieve
large uniform elongations. For a metallic glass, dislocations do not exist at all due to the lack of
long range crystalline order. For nanocrystalline metals, dislocations can carry some fraction of
the overall plastic strain but they are absorbed after traversing grains and leave no residual
dislocation density.
In addition, the smallest nanocrystalline grains deform through direct
rotation or sliding. While the existence of shear banding in both materials and the similarities
between their overall mechanical behavior is important, the evolution of grain structure is our
main finding in this paper.
9
Our observations of structural evolution inside of nanocrystalline shear bands show that
intense strain localization leads to (1) grain growth and (2) the formation of a shear texture. The
first type of evolution can be understood as the material being driven closer to an equilibrium
state by high stresses during deformation. Atoms in the grain boundaries are defects and exist in
a higher energy state than atoms found in the grain interiors. Grain growth reduces the volume
fraction of material located inside of grain boundaries, although the extent of grain growth will
be a complex convolution of effects relating to the active deformation mechanisms and the
driving force for growth. For a starting grain size of 5 nm, plasticity should be dominated by
grain rotation and sliding, as well as grain boundary migration33,34,35. These mechanisms are able
to efficiently coarsen grain structures, with grain rotation capable of causing grain
coalescence36,37 and boundary migration directly increasing the size of one grain at the expense
of another. Rupert18 used MD simulations to demonstrate that such mechanisms can cause grain
growth during strain localization in polycrystalline nanowires with grain sizes similar to those
studied here. However, as grains grow, there will be a gradual shift toward dislocation-based
plasticity. Vo et al.38 found that dislocation-based plasticity become the majority carrier of
plastic strain as grains become larger than ~10 nm. Therefore, the grain growth will effectively
shut itself off once grains are too large for collective grain boundary mechanisms to dominate
plasticity. This idea is supported by our observation that the maximum grain size stayed below
20 nm in both nanoindentation and microcompression experiments. Another contributing factor
could be supersaturation of the grain boundaries.
Previous work by Detor and Schuh21
demonstrated that only ~17-18 at.% W is enough to stabilize a d = 8 nm microstructure in
nanocrystalline Ni-W, while our alloy here has 23 at.% W for this same grain size after
coarsening. Considering that the increase in grain size has decreased the volume fraction of
10
grain boundaries, and our careful examination of SAED patterns of shear bands shows no
evidence of any second phase segregation or formation of W particles39, the concentration of W
at the grain boundaries should be even higher than the minimum value needed for thermal
stability. With additional grain boundary doping, there will be a further decrease in the grain
boundary energy, reducing the driving force for coarsening of the nanocrystalline structure.
Microstructural evolution toward a lower energy state is also observed in metallic
glasses, where nanocrystalline structures are sometimes found inside or in the vicinity of shear
bands40. For example, Jiang et al.10,41 and Kim et al.42 saw that small crystallites nucleated in
indented regions of Al- and Zr-based bulk metallic glasses, respectively. Zheng et al.43 also
observed shear bands with nanocrystals inside of a MgCuGd metallic glass consolidated with
high pressure torsion (HPT), where a material is deformed in a torsional mode while under a
confining pressure. During shear banding, the atoms which were originally in an amorphous
configuration have the ability to settle into a crystalline state. Most studies suggest that this
evolution process is related to the creation of excess free volume, enhanced atomic shuffling, and
high local strain rates inside of the shear bands
40,41,44
. However, other authors have found that
local temperature rise inside of shear bands can cause crystallization, and this temperature rise is
often accompanied by the formation of vein patterns or liquid like droplets45,46 on the surface of
the sheared specimen. Evolution driven by local temperature fluctuations will also result in
diffuse shear bands, with gradual structural evolution as one moves away from the band40.
However, our experimental observations suggest that such local temperature rise is not a
contributing factor to the structural evolution in nanocrystalline Ni-W. SEM images of the
failure surfaces from the microcompression samples showed no vein patterns and the slip
surfaces resembled a clean fracture. In addition, our TEM images showed shear bands with
11
well-defined edges and no gradient in the microstructure was found in the vicinity of the shear
bands. As such, it appears that our evolution is purely driven by mechanical stresses.
The observation of texture formation can be explained by a shift to dislocation-based
mechanism through a combination of grain growth and high plastic strains. Previous studies47,48
have shown that plasticity due to grain boundary sliding and grain rotation randomizes texture,
similar to observations of superplastic behavior in nanocrystalline metals49. However, once
grains get larger than ~10 nm38, plasticity is dominated by dislocation glide, which has been
shown to induce preferred orientation (see, e.g., the formation of simple shear texture
in
nanocrystalline Ni50). The dominant deformation mechanism is also a function of plastic strain,
with higher plastic strains increasing the importance of dislocation-based mechanisms38. This
concept is supported by literature data from processing experiments. For example, Ivanisenko et
al.47 employed HPT on a nanocrystalline Pd and found that extremely high shear strains of 124
can result in grain growth and texture formation. However, Markmann et al.48 showed that cold
rolling of a similar nanocrystalline Pd to much lower plastic strain values does not cause any
texture formation. Skrotzki et al.51 studied the effect of severe plastic deformation on the texture
of nanocrystalline Pd-Au more systematically, finding that a random texture was observed at low
applied strains. This was then replaced by a “brass-type” shear texture once the applied shear
strain exceeded 1.
The effect of the overall stress state can be understood by comparing the results of the
microcompression with those of the nanoindentation. While a microcompression experiment
applies a simple uniaxial stress to the micropillar, the indentation stress state is much more
complicated under the indenter tip, having a combination of hydrostatic and deviatoric stress
components. In addition, the stress-strain curve for microcompression shows that the only
12
deviation from elasticity is discrete plastic deformation through shear banding. As mentioned in
the Results section, there is a combination of homogeneous plasticity and shear banding in the
case of our nanoindentation experiments. We find that the nanoindentation curve is smooth with
just less than 10 displacement bursts caused by shear bands, each only ~10-15 nm in length.
Additional experiments with even lower strain rates and higher data acquisition rates, which
should make it easier to activate and identify shear bands, also showed the same behavior. If
shear banding was the only contributor to plastic deformation, subtracting the pop-in
displacements from the load-displacement curve would give a loading curve that is predicted by
Hertzian elasticity theory and negligible residual indentation depth after unloading. This is
clearly not the case for our experiments on Ni-W, as a large plastic impression is left on the
surface even through shear banding should only contribute ~100 nm of plastic depth.
Shear banding in nanoindentation experiments, in contrast to microcompression, cannot
be responsible for all of the plastic deformation. Therefore, homogenous plasticity outside of the
shear bands must have occurred during nanoindentation. However, by looking at the grain size
distribution outside of the shear bands but within the plastic zone of the indentation, we find that
homogenous plasticity does not drive structural evolution, as the average grain size and even the
details of the grain size distribution are identical to the as-deposited microstructure.
This
observation contrasts with previous observations of pure nanocrystalline metals, which
experience grain growth during the early stages of plasticity in uniaxial tension experiments22.
Doping of grain boundaries with W makes the microstructure stable against coarsening at small
plastic strains, analogous to the increase in thermal stability, but this structural stability can be
overcome when intense shear localization occurs. These results suggest that the microstructure
13
of even thermally-stable nanocrystalline FCC alloys should be considered dynamic, if extreme
deformation conditions such as catastrophic shear banding can be accessed.
To summarize, the effects of shear banding on local grain structure were studied in a
nanocrystalline Ni-W alloy with an as-deposited grain size of 5 nm.
Microcompression
experiments as well as nanoindentation tests were used to study the effects of different stress
fields and deformation boundary conditions. Evidence of significant grain growth and texturing
as a result of strain localization was found inside of the shear bands. A degree of mechanicallyinduced grain growth was observed for both testing conditions, suggesting an inherent limit on
this coarsening behavior that depends on multiple factors such as the dominant deformation
physics and the driving force for grain growth, both of which change with grain size. Our results
showed that the nanocrystalline Ni-W can be susceptible to grain growth only when extreme
values of shear strain are applied, and suggest that this is a purely stress-driven process and not
caused by local heating inside the shear bands.
Methods
A Ni-based alloy with 23 at.% W and an average grain size of 5 nm was prepared using
the pulsed electrodeposition method of Detor and Schuh21. Although the equilibrium Ni-W
phase diagram predicts a mixture of FCC Ni(W) solid solution and Ni4W for this alloy
composition, our films were comprised only of FCC Ni(W) solid solution, in line with previous
observations of similar nanocrystalline Ni-W alloys
25,39
. Cylindrical micropillars with average
diameters of 7 µm and lengths of 16 µm were fabricated using a lathe milling Focused Ion Beam
(FIB) technique11. An Agilent G200 nanoindenter with a flat triangular tip was used to compress
the pillars at a constant displacement rate of 5 nm/s. For our nanoindentation studies, a cube
14
corner tip was used to make the observation of the deformed region around the indent easier, as
significant pile-up can occur with this tip geometry52. Previous studies30,53 have shown that
shear banding during nanoindentation is strain rate dependent and that a higher strain rate shifts
the plasticity toward more homogenous plasticity. For this reason, a relatively low strain rate of
0.05 s-1 was chosen to promote shear banding. For nanoindentation, the as-deposited sample was
annealed at 300°C for 1 hour to relax the grain boundary structure to a lower energy level52 since
relaxation has been shown to increase the propensity for shear localization.
TEM
characterization was performed with a Philips-FEI CM-20 operated at 200 kV and equipped with
a Gatan digital camera. Site-specific TEM samples were prepared using a FIB in-situ lift out
technique54 in a FEI Quanta 3D field emission gun (FEG) dual beam microscope. The TEM
lamellas were polished with a 5 kV Ga+ ion beam to minimize ion beam damage to the sample.
All SEM imaging was carried out at 5 kV in the same dual beam SEM/FIB.
Acknowledgments
This work was supported by the U.S. Army Research Office, through Grant W911NF-12-1-0511.
Author contributions
A.K. carried out the experimental work. All authors contributed to discussion and analysis of the
data, as well as manuscript writing.
Additional information
Competing financial interests: The authors declare no competing financial interests
15
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Figure 1. Microcompression of nanocrystalline Ni-W with an average grain size of 5 nm:
(a) SEM image of a micropillar after deformation, taken at 52° tilt. Several slips steps from
primary shear bands are observed on the surface, in addition to smaller, secondary shear bands
criss-crossing in between. (b) True stress-strain curve of the corresponding pillar showing
several displacement bursts during microcompression.
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Figure 2. Microstructure of the shear bands inside the pillar: (a) TEM image of a primary
shear band outlined with dashed white lines and secondary shear band outlined with solid white
lines. (b) Magnified view of the area denoted by the white box in (a) showing grain growth
inside of the shear band. (c) Cumulative distribution function of grain size from grains inside
and outside the shear bands, as well as the as-deposited sample. (d) TEM image showing an
example of the shear band network inside of the pillar.
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Figure 3. Pure shear texture in the shear band: (a) Selected area diffraction pattern taken
from a thick shear band. (b) Corresponding dark field TEM image of the shear band, showing
many grains with the preferred texture within the shear bands. (c) Magnified view of the
microstructure inside the shear band, showing a cluster of grains with similar orientations.
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Figure 4. Nanoindentation of nanocrystalline Ni-W with average grain size of 5 nm using a
cube corner tip: (a) SEM image of one of the indents taken at 30° tilt. (b) Corresponding
nanoindentation load-displacement curve, with several strain bursts denoted by black arrows. (c)
Average strain rate versus indentation depth for the same loading curve, showing jumps in the
instantaneous strain rate during loading which match up with the bursts denoted in (b).
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Figure 5. TEM images of Ni-W after nanoindentation: (a) TEM image of the entire
indentation cross-section. (b) Magnified image of the dashed box showing the shear bands
diretly underneath the indenter tip. (c) Magnified image of the solid box, showing shear bands
which terminate at the surface and create slip steps.
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Figure 6. Microstructure after nanoindentation: (a) The microstructure of the same indent in
the pile-up on the surface of the sample; TEM image of shear bands forming an intersecting
network underneath an indent. (b) Cumulative distribution function of grain size Cumulative
fraction vs. grain size from grains inside and outside the shear bands, as well as the original asdeposited relaxed microstructure.
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